a) Consider three consumers who care about the consumption of a private good and their consumption...

 

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a) Consider three consumers who care about the consumption of a private good and their consumption of a public good. Their utility function are given by U = X,G i=1, 2, 3 Where X, is consumer i's consumption of the private good and G is the amount of the public good consumed by all. The unit cost of the private good is K1 and the unit cost of the public good is K10. Individual wealth levels are w = 30, w = 50 and w;= 20. 1). Compute the marginal rate of substitution between G and X for each of the three consumers. i). Derive the Samuelson condition for this model (4 Marks) (4 Marks) iii). Derive the aggregate resource constraint and compute the optimal level of public good consumption. (7 Marks) a) Consider three consumers who care about the consumption of a private good and their consumption of a public good. Their utility function are given by U = X,G i=1, 2, 3 Where X, is consumer i's consumption of the private good and G is the amount of the public good consumed by all. The unit cost of the private good is K1 and the unit cost of the public good is K10. Individual wealth levels are w = 30, w = 50 and w;= 20. 1). Compute the marginal rate of substitution between G and X for each of the three consumers. i). Derive the Samuelson condition for this model (4 Marks) (4 Marks) iii). Derive the aggregate resource constraint and compute the optimal level of public good consumption. (7 Marks)